calculus of variations
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In this lecture, Leonard Susskind continues his discussion of Einstein's theory of general relativity. He also gives a broad overview of the field of tensor calculus and it's relation to the curvature and geometry of space-time.
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Intuition behind the motion of a mass on a spring (some calculus near the end).
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August 9, 2007 presentation by Russ Altman for the Stanford University Office of Science Outreach's Summer Science Lecture Series. There are a number of causes for variation in drug response across the population, but differences in genetics are an important factor. Russ Altman, Professor & Chair of Bioengineering and Professor of Genetics and Medicine, discusses how variations in genetics can alter the "typical" response as well as touch...more
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Professor Shankar introduces the course and answers student questions about the material and the requirements. He gives an overview of Newtonian mechanics and explains its two components: kinematics and dynamics. He then reviews basic concepts in calculus through two key equations: x0 + v0t + ½ at2 and v2 = v02+ 2 a (x-x0), tracing the fate of a particle in one dimension along the x-axis.
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The discussion of suicide continues. A few more cases are introduced to consider circumstances under which it might be rational to end one's life, and more graphs are drawn that show relevant variations in the quality of one's life. A question is then posed about how one should make a decision about continuing or ending life, given that one cannot know the future with certainty. Finally, two quick moral arguments concerning suicide which r...more
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Highlights of Calculus is a series of short videos that introduces the basic ideas of calculus — how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject.
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We first apply our big idea--backward induction--to analyze quantity competition between firms when play is sequential, the Stackelberg model. We do this twice: first using intuition and then using calculus. We learn that this game has a first-mover advantage, and that it comes commitment and from information in the game rather than the timing per se. We notice that in some games having more information can hurt you if other players know y...more
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This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
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This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.
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Behavioral Finance is a relatively recent revolution in finance that applies insights from all of the social sciences to finance. New decision-making models incorporate psychology and sociology, among other disciplines, to explain economic and financial phenomenon, such as erratic stock price variations. Psychological patterns such as overconfidence and perceived kinks in the value function seem to impact financial decision-making, but are...more
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Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes.
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This is a series of lectures for MATH2111 "Higher Several Variable Calculus" and "Vector Calculus", which is a 2nd-year mathematics subject taught at UNSW, Sydney. This playlist provides a shapshot of some lectures presented in Session 1, 2009. These lectures focus on presenting vector calculus in an applied and engineering context, while maintaining mathematical rigour. Thus, this playlist may be useful to students of mathematics, but als...more
